A committee is to be chosen from a group of 11 women and 14 men. How many ways can they select a president, treasurer, and secretary, if the treasurer and secretary must be females? No person can serve in more than one position.
case 1 -- the president is a man
C(14,1) x C(11,1) x C(10,1)
= 14x11x10 = 1540
case 2 -- the president is a woman
C(11,1) x C(10,1) x C(9,1) = 990
Number of possible committees = 1639
To find the number of ways they can select a president, treasurer, and secretary, we need to consider the number of choices for each position.
First, let's find the number of choices for the president. Since there are 11 women and 14 men in the group, we have 11 + 14 = 25 people to choose from. Any person in the group can be the president. Therefore, there are 25 choices for the president.
Next, let's find the number of choices for the treasurer. Since the treasurer must be a female, we have 11 women to choose from. After selecting one woman as the treasurer, there will be 10 women remaining.
Finally, let's find the number of choices for the secretary. Similar to the treasurer, the secretary must also be a female, so there are 10 remaining women to choose from.
To calculate the total number of ways to select a president, treasurer, and secretary, we multiply the number of choices for each position:
Number of choices for president * Number of choices for treasurer * Number of choices for secretary
= 25 * 11 * 10
= 2750
Therefore, there are 2750 ways to select a president, treasurer, and secretary with the given conditions.